General Theory for Nonlinear Operators in Self-Supervised Inverse Problems

Empirical characterization of SSL loss behavior under linear, phase retrieval, quantized sensing, and sigmoid operators

4
Operator Types
2.5x
Phase Retrieval Cond. Ratio
0.1
Linearity Radius
5
Measurement Ratios

Convergence Comparison

SSL Loss During Reconstruction

Local Linearity Assessment

Linearization Error vs Perturbation Radius

Complexity Hierarchy

OperatorCondition NumberLoss CurvatureFinal MSE
Linear8.6Low0.269
Sigmoid8.6Low0.171
Phase Retrieval21.1Medium0.218
Quantized Sensing>10^6High0.157

Measurement Ratio Study

MSE vs Measurement Ratio (m/n)